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Prove that if the 3 altitudes of a triangle are equal then the triangle is equilateral.
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 one year ago
 one year ago
Prove that if the 3 altitudes of a triangle are equal then the triangle is equilateral. See attachment
 one year ago
 one year ago

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mathsloverBest ResponseYou've already chosen the best response.1
I tried to do this and have got so far that AB = AC
 one year ago

mathsloverBest ResponseYou've already chosen the best response.1
I took following triangles :ABF and AEC by AAS I got both of these triangles congruent and therefore by CPCT AB = AC
 one year ago

mathsloverBest ResponseYou've already chosen the best response.1
(CPCT = Congruent Parts of Congruent Triangles are equal)
 one year ago

joemath314159Best ResponseYou've already chosen the best response.1
That idea should work to get that AB=BC as well.
 one year ago

mathsloverBest ResponseYou've already chosen the best response.1
So far , we have got ABC as isosceles. Now, I took triangle ABC and AFC both of these triangles are congruent by RHS BF = FC ( by CPCT ) therefore F is mid point of BC an AF is median and altitude also Therefore , this is the property of an equilateral triangle , so ABC is an equi. triangle
 one year ago

mathsloverBest ResponseYou've already chosen the best response.1
You mean to take ABE and BEC triangles @joemath314159 ?
 one year ago

joemath314159Best ResponseYou've already chosen the best response.1
yep. and do exactly what you did with the other triangles again.
 one year ago

mathsloverBest ResponseYou've already chosen the best response.1
I meant this : ADC and ABD in the above comment.
 one year ago

mathsloverBest ResponseYou've already chosen the best response.1
I think I had tried that earlier but I didnt' get any favorable result , wait let me do it again
 one year ago

joemath314159Best ResponseYou've already chosen the best response.1
there are many combinations you could take. The pair I see is triangles BEC and BDA.
 one year ago

mathsloverBest ResponseYou've already chosen the best response.1
Oh yes that will work ... BEC and BDA .. this gives some output to me.
 one year ago

mathsloverBest ResponseYou've already chosen the best response.1
Thanks a lot @joemath314159 for your help .. Might gonna work in more concentration for me..
 one year ago
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